I looked up the Basilica and thought you could get there by Metro. If that's not true, I should probably let Matthew know. My online research (not always the most reliable) said there was a Metro stop 0.4 miles away.
There is a metro stop close to the chapel, but I am not sure if it goes all the way to the Basilica...
I am not too familiar with the D.C. area though, and put this here because a friend of mine asked me to post the the information for them...
I just looked the area up, and is seems that the Basilica it is about a half hour walk from the metro. So, as long as they are good with that it should not be too bad. :)